Políticas de conservación y gestión ambiental en áreas protegidas 61-

Algorithms matching images on the basis of edge finder output invariably place boundaries where there are step-edge-like responses, e.g. at peak responses of a first difference operator or zero-crossing of second difference operator. How-ever, other types of edge information can be detected and there is some evidence that they should be used in matching. For example, Mayhew and Frisby 1981) present psychophysical data suggesting that humans must be using information in addition to step-edge boundaries when matching stereo 'images. They suggest that this additional information may consist of locations of peaks and troughs in the second derences. Watt and Morgan 1983) make a similar suggestion, based on psychophysical experiments on human perception of edge blur.

The Phantom edge finder detects both zero-crossing and roof edge responses, but my matcher uses only zero-crossing boundaries are used in my matcher im-plementation. There are at least two ways that roof edge information could be incorporated. The stereo matcher could be extended to use roof edge informa-tion directly. Alternatively, the matching program could use locainforma-tions of all label transitions, not just zero-crossings, as boundaries. This would allow responses of both types to be used together in matching. Classification of responses into roof edges vs. zero-crossings would then be postponed until after stereo fusion. This solution might be able to account for Mayhew and Frisby's 1981) data, though additional experimentation would be required to test this.

Chapter 11 more thoroughly than the other applications presented in the thesis.

Finally, 'it is interesting as a possible solution to problems that are both central to visual analysis and difficult for existing computer algorithms to handle. The acid test of its performance comes in Chapters 6 9 and 10, when the matcher 'is applied to analysis of stereo images and to edge finder evaluation. I summarize the other points in this section.

The matching algorithm developed 'in this chapter directly tests one cen-tral hypothesis of this thesis, that topological structure is important 'in solving practical reasoning problems. Equivalence of topological structure is the main constraint on the matching process. If the only requirements were that labels be preserved and the correspondence not deviate much from the oginal alignment, considerable scrambling of images would be possible. Using this constraint, the algorithm makes a sharp and intuitively reasonable dstinction between matches and non-matches. This is illustrated by the results presented in this chapter and later chapters. In particular, the results of edge finder testing presented in Chap-ter 9 show convincingly that the algorithm consistently 'ects matches between two random noise patterns, but not between two copies of the same signal, even when slightly corrupted by noise.

The analysis phase of the stereo computation also contains several algorithms that use connectivity. Two of these algorithms measure the size of a connected neighborhood. The matching strength computation measures the area of star-convex match neighborhoods, whereas measurement of boundary motion mea-sures the length of a connected path through an adjustment region. Further-more motion measurements are interpolated and smoothed by algorithms that are constrained not to cross boundaries. Thus, in addition to the use of the full topological structure in the adjustment phase, the matcher also offers more

examples of uses of connectivity smilar to those in the edge finder described 'in Chapter 4.

The development of boundary adjustment operations, unlike most other ap-plications presented in this thesis, fully exercises the mathematical machinery developed in Chapter 11. Although the idea of using boundary topology has been proposed before (particularly 'in stereo matching), previous researchers have not been able to provide a sufficiently clear or powerful formulation to make full use of the idea. To attack matching in the way that I dd requires a large in-vestment in mathematical machinery and development of techniques for building algorithms. This investment would never have made sense without the additional context of problems from other domains requiring similar machinery.

1. Introduction

As we saw 'in Chapter 3 the task n stereo matching is to establish a corre-spondence between two images of the same scene taken from slightly different viewpoints. In this chapter, I present a new stereo matching algorithm based on the image matcher discussed in Chapter 5. We have seen how this matcher can compare two images at one fixed agnment. This chapter describes the control structure needed to search a series of alignments to locate good matches.

Stereo matching is a good domain for testing the image matcher, because it 'is a well-studied problem and the correct answer to each matching task 'is relatively clear. Some evaluation problems still ase. For example, what people see in a synthetic stereogram rarely corresponds exactly to the input depth specifications.

However, since stereograms produce vivid subjective perceptions, the desired out-put 'is much clearer to human observers thanin tasks such as inter-scale matching.

Furthermore, substantial psychophysical data about human stereo perception is available. This data is useful in making design decisions for computer algorithms.

This chapter begins with an overview of the control structure used in the stereo algorithm. This control structure consists of two parts. First, camera positions are adjusted and the algorithm chooses the set of alignments at which to search for matches. This i's described in Section 3 and compared to previous algorithms in Section 4. After atching is done at each alignment, the results

from different alignments must be combined. This process is described in Sec-tion 5. SecSec-tions 6 and 7 discuss types of matching constraints used in previous stereo algorithms and analyze how they are related to the constraints used in my implementation.

As I mentioned 'in Chapter 3 the new stereo matcher offers two advantages over previous algorithms. First, the topological continuity constraint makes its match evaluations more robust. This aows it to disambiguate larger numbers of candidate matches without becoming confused. Secondly, the matcher requires support neighborhoods for strength and dsparity to be connected sets of cells at a similar disparity. This prevents results for cells near depth boundaries from being contaminated by values on the other side of the boundary. Chapter 0 presents detailed results of the stereo algorithm's performance on both natural and synthetic 'images. It also shows an example of how an adaptation of the algorithm might be used for motion analysis.